Y(y-1)-(y-5)²=2

To solve the equation \( y(y - 1) - (y - 5)^2 = 2 \), we will first simplify the left-hand side of the equation. 1. Expand \( y(y - 1) \): \[ y(y - 1) = y^2 - y \] 2. Expand \( (y - 5)^2 \): \[ (y - 5)^2 = y^2 - 10y + 25 \] 3. Substitute these expansions back into the equation: \[ y^2 - y - (y^2 - 10y + 25) = 2 \] 4. Distribute the negative sign: \[ y^2 - y - y^2 + 10y - 25 = 2 \] 5. Combine like terms: \[ 9y - 25 = 2 \] 6. Add 25 to both sides: \[ 9y = 27 \] 7. Divide by 9: \[ y = 3 \] Thus, the solution to the equation \( y(y - 1) - (y - 5)^2 = 2 \) is: \[ \boxed{3} \]